Answer:
y = 2cos5x-9/5sin5x
Step-by-step explanation:
Given the solution to the differential equation y'' + 25y = 0 to be
y = c1 cos(5x) + c2 sin(5x). In order to find the solution to the differential equation given the boundary conditions y(0) = 1, y'(π) = 9, we need to first get the constant c1 and c2 and substitute the values back into the original solution.
According to the boundary condition y(0) = 2, it means when x = 0, y = 2
On substituting;
2 = c1cos(5(0)) + c2sin(5(0))
2 = c1cos0+c2sin0
2 = c1 + 0
c1 = 2
Substituting the other boundary condition y'(π) = 9, to do that we need to first get the first differential of y(x) i.e y'(x). Given
y(x) = c1cos5x + c2sin5x
y'(x) = -5c1sin5x + 5c2cos5x
If y'(π) = 9, this means when x = π, y'(x) = 9
On substituting;
9 = -5c1sin5π + 5c2cos5π
9 = -5c1(0) + 5c2(-1)
9 = 0-5c2
-5c2 = 9
c2 = -9/5
Substituting c1 = 2 and c2 = -9/5 into the solution to the general differential equation
y = c1 cos(5x) + c2 sin(5x) will give
y = 2cos5x-9/5sin5x
The final expression gives the required solution to the differential equation.
uppose that the length of 20 years worth of baseball games has been investigated, and that it has been found that the average (mean) length of a game is 165 minutes and the standard deviation is 30 minutes. What is the probability that a randomly selected game will last between 120 and 210 minutes
Answer:
P(120< x < 210) = 0.8664
Step-by-step explanation:
given data
time length = 20 year
average mean time μ = 165 min
standard deviation σ = 30 min
randomly selected game between = 120 and 210 minute
solution
so here probability between 120 and 210 will be
P(120< x < 210) = [tex]P(\frac{120-165}{30}< \frac{x-\mu }{\sigma } <\frac{210-165}{30})[/tex]
P(120< x < 210) = [tex]P(\frac{-45}{30}< \frac{x-\mu }{\sigma } <\frac{45}{30})[/tex]
P(120< x < 210) = P(-1.5< Z < 1.5)
P(120< x < 210) = P(Z< 1.5) - P(Z< -1.5)
now we will use here this function in excel function
=NORMSDIST(z)
=NORMSDIST(-1.5)
P(120< x < 210) = 0.9332 - 0.0668
P(120< x < 210) = 0.8664
12 and 3/6 -5 and 2/12
Answer:
7.33333333333 I think. Hope this helped.
The function f determines the volume of the box (in cubic inches) given a cutout length (in inches). Use function notation to represent the volume of the box (in cubic inches) when the cutout length is 0.2 inches. Use function notation to represent the volume of the box (in cubic inches) when the cutout length is 1.3 inches. Use function notation to represent how much the volume of the box (in cubic inches) changes by if the cutout length increases from 0.2 inches to 1.3 inches. Use function notation to represent how much the volume of the box (in cubic inches) changes by if the cutout length increases from 5.5 inches to 5.6 inches.
Complete Question
A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides. However, the size of the paper is unknown!
Answer:
(a)[tex]f(0.2)=0.2(l-0.4)(w-0.4)[/tex]
(b)[tex]f(1.3)=1.3(l-2.6)(w-2.6)[/tex]
(c)f(1.3)-f(0.2)
(d) f(5.6)-f(5.5)
Step-by-step explanation:
Let the Length of the paper =l (in inches)
Let the Width of the paper =w (in inches)
Let the length of the cutout square = x (in inches)
Base Length of the Box = l-2xBase Width of the box =w-2xHeight of the box =xVolume of the box: [tex]f(x)=x(l-2x)(w-2x)[/tex]
(a)When the cutout length is 0.2 inches.
x=0.2
Volume of the box (in cubic inches) ,
[tex]f(0.2)=0.2(l-0.4)(w-0.4)[/tex]
(b)When the cutout length is 01.3 inches.
x=1.3
Volume of the box (in cubic inches) ,
[tex]f(1.3)=1.3(l-2.6)(w-2.6)[/tex]
(c)If the cutout length increases from 0.2 inches to 1.3 inches.
Change In volume (in cubic inches):
[tex]f(1.3)-f(0.2)\\=1.3(l-2.6)(w-2.6)-0.2(l-0.4)(w-0.4)[/tex]
(d)If the cutout length increases from 5.5 inches to 5.6 inches.
Change In volume (in cubic inches):
[tex]f(5.6)-f(5.5)\\=5.6(l-11.2)(w-11.2)-5.5(l-11)(w-11)[/tex]
Please answer this correctly
Answer:
Chicken: 36%
Beef: 34%
Black Bean: 30%
Hope this helps!
Look at the work shown for the division problem shown on the right. The remainder is 8 . Now, evaluate f (x) = 2x4 – 4x3 – 11x2 + 3x – 6 for x = –2. f (–2) = 8 Compare the values you entered above. f (–2) is the remainder when dividing the polynomial by x + 2. Divide 2x4- 4x3 - 11x2 + 3x - 6 by x + 2.
Answer:
1st : 8
2nd: 8
3rd: equal to
Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
The remainder of the polynomial when divided by x + 2 is -60.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
2[tex]x^{4}[/tex] - 4x³ - 11x² + 3x - 6 divide by x + 2.
Now,
x + 3 ) 2[tex]x^{4}[/tex] - 4x³ - 11x² + 3x - 6 ( 2x³ - 2x² - 5x + 18
2[tex]x^{4}[/tex] + 6x³
(-) (-)
-2x³ - 11x² + 3x - 6
-2x³ - 6x²
(+) (+)
- 5x² + 3x - 6
-5x² - 15x
(+) (+)
18x - 6
18x + 54
(-) (-)
-60
We see that,
The remainder is -60.
f(-2) = 2[tex]x^{4}[/tex] - 4x³ - 11x² + 3x - 6
f(-2) = 2 x 16 + 32 - 44 - 6 - 6 = 32 + 32 - 44 - 12 = 64 - 56 = 8
Thus,
The remainder of the polynomial when divided by x + 2 is -60.
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The currency in Bolivia is the Boliviano. The exchange rate is approximately $1 = 8 Bolivianos. At this rate, how many Bolivianos would you get if you exchanged $3?
Answer:
24 bolivianos
Step-by-step explanation:
$1=8b
$3=?
Cross multiply: ($3*8)/1 =24
Which of the following is a subset of every set? * 1)Universal Set 2)Null Set 3)Both of these 4)None of these
Answer:
[tex]1[/tex]
Step-by-step explanation:
Universal set contains all elements and of which all other sets are subsets.
which of the following describes the zeroes of the graph of f(x)= -x^5+9x^4-18x^3
Answer:
[tex]-x^5+9x^4-18x^3=0\\-x^3(x^2-9x+18)=0\\-x^3(x-3)(x-6)=0\\\\\\\\x=0\\x=3\\x=6[/tex]
Use the following cell phone airport data speeds​ (Mbps) from a particular network. Find the percentile corresponding to the data speed 11.2 Mbps. 0.1 0.2 0.2 0.3 0.4 0.4 0.4 0.5 0.5 0.6 0.6 0.8 0.9 0.9 0.9 1.1 1.3 1.7 1.8 1.9 2.3 2.4 2.5 2.6 2.7 3.1 3.5 3.5 3.7 3.8 4.8 5.2 7.4 7.9 8.2 8.6 9.3 11.2 11.3 11.4 12.1 12.6 13.1 13.3 13.6 13.8 14.6 15.6 15.7 25.6
Answer: the percentile is 74%
Step-by-step explanation:
The given data distribution is arranged in increasing order as:
0.1 0.2 0.2 0.3 0.4 0.4 0.4 0.5 0.5 0.6 0.6 0.8 0.9 0.9 0.9 1.1 1.3 1.7 1.8 1.9 2.3 2.4 2.5 2.6 2.7 3.1 3.5 3.5 3.7 3.8 4.8 5.2 7.4 7.9 8.2 8.6 9.3 11.2 11.3 11.4 12.1 12.6 13.1 13.3 13.6 13.8 14.6 15.6 15.7 25.6
The total number of values given in the data is 50
Percentile = number of values in the distribution lesser than the given value × 100/ total number of values in the distribution
Considering the data speed of 11.2 Mbps, the number of data speed lower than 11.2 is 37
Percentile = (37 × 100)/50 = 74%
which ordered pair is a solution for 2x+5y=-11
10x+3y=11
Answer:
X = 2 and Y = -3
Step-by-step explanation:
2x+5y=-11 - equation 1
10x+3y=11 - equation 2
from equation 1, 2X = -11 - 5y
X = -11/2 - 5Y/2
X = -5.5 - 2.5Y
insert X = -5.5 - 2.5Y into equation 2
therefore, 10x+3y=11
10(-5.5 - 2.5Y) + 3y = 11
-55 -25Y +3Y = 11
-22Y = 11+55
Y = -66/22
Y = -3
insert Y = -3 into equation 1
thus 2x + 5(-3) = -11
2x - 15 = -11
2x = -11 + 15
2x = 4
x = 4/2
x = 2
ordered pair: X = 2 and Y = -3
What is the slope of a line that is perpendicular to the line y = -1/2x + 5?
the answer choices are
-2
-1/2
1/2
2
Answer:
2
Step-by-step explanation:
as you can see the slope of the line y = -1/2x + 5 is -1/2
the slope m of any line perpendicular to it should verify : -1/2×m = -1
-1/2×m = -1
→ multiply both sides by -2
m = 2
What is the length of the line?
Answer:
B) 5
Step-by-step explanation:
The points are (2,2) and (6,5). Subtract both Y's and X's and then square the answers and add. you should get 25, which has a square root of 5.
A trapezoid is shown. The lengths of the bases are 4 and 8. The height of the altitude is 4. What is the area of the trapezoid?
Answer:
24
Step-by-step explanation:
Formula
The area of a Trapezoid is given as
A = (b1 + b2)*h/2
Givens
b1 = 8
b2 = 4
h = 4
Solution
Area = (8 + 4)*4/2
Area = 12*4/2
Area = 24
Suppose that the raw daily oxygen purities delivered by an air-products supplier have a standard deviation LaTeX: \sigma\approx.1 σ ≈ .1 (percent), and it is plausible to think of daily purites as independent random variables. Approximate the probability that the sample mean LaTeX: \frac{ }{X} X of n = 25 delivered purities falls within .03 (percent) of the raw daily purity mean, LaTeX: \mu μ .
Answer:
There is a probability of 86.6% that the sample mean falls within 0.03 percent of the raw purity mean.
Step-by-step explanation:
We have a population standard deviation of σ ≈ 0.1.
We have a sample of size n=25.
Then, we have a sampling distribution, which has a standard deviation for the sample mean that is:
[tex]\sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{0.1}{\sqrt{25}}=\dfrac{0.1}{5}=0.02[/tex]
Now, we can calculate a z-score for a deviation of 0.03 percent from the mean as:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{0.03}{0.02}=\dfrac{0.03}{0.02}=1.5[/tex]
Note: we considered that the margin is ±0.03.
Then, the probability is:
[tex]P(|X-\mu|<0.03\%)=P(|z|<1.5)=0.866[/tex]
For an exam given to a class, the students' scores ranged from 34 to 99 , with a mean of 78 . Which of the following is the most realistic value for the standard deviation: -14,3,0,56,15?
Clearly explain what's unrealistic about each of the other values.
Answer:
The most realistic value for the standard deviation is 15.
Step-by-step explanation:
The standard deviation of a distribution is a measure of dispersion. It is a measure of the spread of the distribution from the mean of the distribution. It expresses how far most of the distribution is from the mean.
Mathematically, the standard deviation is given as the square root of variance. And variance is an average of the squared deviations from the mean.
Mathematically,
Standard deviation = σ = √[Σ(x - xbar)²/N]
x = each variable (ranges from 34 to 99)
xbar = mean = 78
N = number of variables
Now taking the given possible values of the standard deviation one at a time,
-14
The standard deviation cannot be negative as it is a square root of the average of the sum of square deviations from the mean. Since the square of a number cannot be negative, it directly translates that the standard deviation cannot be negative.
3
A small standard deviation like 3 indicates that the distribution mostly centres about the mean, with very little variation. And the distribution given has a mean (78) that is very far away from at least one of the variables in the distribution. Hence, 3 is too low to pass ad the standard deviation of this distribution described.
0
A standard deviation of 0 indicates that all the variables in the distribution have the same value as the mean. That is, the distribution only contains 1 number, probably multiple times. So, this cannot be the standard deviation for the distribution described.
56
This value represents a value that is too high to express the spread of the distribution described. The mean (78) is very close to the maximum value of the distribution, and far away from the lower value(s), indicating that most of the distribution is in and around the upper values with a few variables closer to the lower limit. A standard deviation as high as 56 for a mean of 78 translates to a distribution with most of variables far from the mean, which isn't the case here.
Moreso, a simple add of the standard deviation to the mean or subtracting the standard deviation from the mean should give at least one of the results with values within the distribution.
(Mean) + (Standard deviation) = 78 + 56 = 134 >> 99 (outside distribution)
(Mean) + (Standard deviation) = 78 - 56 = 22 << 34 (also outside the distribution)
15
This is the most realistic value for the standard deviation as it represents what the distribution described above is.
The mean (78) being close to the maximum value of the distribution, and far away from the lower value(s) indicates that most of the distribution is in and around the upper values with a few variables closer to the lower limit.
So, 15 indicates a perfect blend of small deviations due to the high values close to the mean and the very high deviation from the evidently few lower values.
(Mean) + (Standard deviation) = 78 + 15 = 93 < 99 (within distribution)
(Mean) + (Standard deviation) = 78 - 15 = 63 > 34 (also within the distribution)
Hope this Helps!!!
When The most realistic value for the standard deviation is 15.
Step-by-step explanation:
Standard deviation The standard deviation of a distribution is a measure of dispersion. also, It is a measure of the spread of the distribution from the mean of the distribution. when It expresses how far most of the distribution is from the mean. Then according to Mathematically, the standard deviation is given as the square root of variance. And also variance is an average of the squared deviations from the mean.mathematically,When Standard deviation is = σ = √[Σ(x - xbar)²/N]After that x = each variable (ranges from 34 to 99)then xbar is = mean = 78Now N is = number of variablesThen we take the given possible values of the standard deviation one at a time, -14 after that The standard deviation cannot be negative as it is a square root of the average of the sum of square deviations from the mean. Since the square of a number cannot be negative, also it directly translates that the standard deviation cannot be negative. After that 3 no when A small standard deviation like 3 indicates that the distribution mostly centers about the mean, with very little variation. And also the distribution given has a mean (78) that is very far away from at least one of the variables in the distribution. Hence proof that is, 3 is too low to pass ad the standard deviation of this distribution described. Then 0 when A standard deviation of 0 indicates that all the variables in the distribution have the same value as the mean. That means is, the distribution only contains 1 number, probably multiple times. So that, this can't be the standard deviation for the distribution described. Now 56 This value represents a value that is too high to express the spread of the distribution described. when The mean (78) is very close to the maximum value of the distribution, and also far away from the lower value(s), indicating that most of the distribution is in and also around the upper values with a few variables closer to the lower limit. when A standard deviation as high as 56 for a mean of 78 translates to a distribution with most of the variables far from the mean, which isn't the case here. More so, when a simple addition of the standard deviation to the mean or subtracting the standard deviation from the mean should have given at least one of the results with values within the distribution.After that (Mean) + (Standard deviation) = 78 + 56 = 134 >> 99 (outside distribution)Then (Mean) + (Standard deviation) = 78 - 56 = 22 << 34 (also outside the distribution) Now last digit 15 This is the most realistic and also a value for the standard deviation as it represents what the distribution described above is.When The mean (78) is close to the maximum value of the distribution, and also far away from the lower value(s) indicates that most of the distribution is in and also that around the upper values with a few variables closer to the lower limit.So that, 15 indicates a perfect blend of small deviations due to the high values close to the mean and also the very high deviation from the evidently few lower values.Then (Mean) + (Standard deviation) = 78 + 15 = 93 < 99 (within distribution) After that (Mean) + (Standard deviation) =Thus, 78 - 15 = 63 > 34 (also within the distribution)
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Tara is graphing the equation 4x + 2y = 10. Which of these shows the correct equation in slope-intercept form, slope, and y-intercept?
Answer:
y = -2x + 5
slope = -2
y intercept = 5
Step-by-step explanation:
Slope intercept form of equation of line is given by y = mx + c
where m is the slope of line
c is the y intercept i.e point where given line intersect y axis.
________________________________________________
given equation 4x + 2y = 10
we have to re-write this equation in form y = mx + c
4x + 2y = 10
subtraction 4x from LHS and RHS
4x + 2y - 4x= 10 - 4x
2y = 10- 4x
we have to eliminate 2 from y for that we
divide LHS and RHS by 2 we
2y /2 = 10/2- 4x/2
y = 5 - 2x
rearranging it in y = mx+c form
y = -2x + 5
thus, m = -2 , c = 5
Mr.Rice students ran a 40 yard dash in the following times 6.8,7.3,7.1 ,7.0,7.2,7.3,7.0 how many race times are recorded
The number of race times recorded as portrayed by the number of data points is seven(7).
What is the number of race times recorded for the dash?From the task content;
It follows that the distance ran be Mr. Rice students was 40 yards.Additionally, it follows from the task content that the times recorded were; 6.8,7.3,7.1 ,7.0,7.2,7.3 and 7.0.
On this note, the number of race times recorded as portrayed by the number of data points is seven(7).
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three friends went to a restraunt and ordered two orders of wings and three soft drinks. their bill totaled $22.50. later that day, five friends went to the same restraunt and ordered three orders of wings and a soft drink each. their bill totaled $34.50. write and solve a system of equations to determine the price of one order of wings.
Answer:
$9
Step-by-step explanation:
Let the price of one order of wings be w.
Let the price for one order of soft drinks be s.
Three friends went to a restaurant and ordered two orders of wings and three soft drinks. Their bill totaled $22.50. This means that:
2w + 3s = 22.50 _____________(1)
Five friends went to the same restaurant and ordered three orders of wings and a soft drink each. Their bill totaled $34.50. This means that:
3w + 5s = 34.50 ______________(2)
We have a system of quadratic equations:
2w + 3s = 22.50 _____________(1)
3w + 5s = 34.50 ______________(2)
Multiply (1) by 5 and (2) by 3:
10w + 15s = 112.50 _______(3)
9w + 15s = 103.50 _______(4)
Subtract (4) from (3):
w = $9
Therefore, the price of one order of wings is $9.
When a feasible region is bounded on all sides, where will the maximum and minimum values of the objective function occur?
at the center of the feasible region
at the top of the feasible region
anywhere within the feasible region
at the vertices of the feasible region
Answer:
Option 4: at the vertices of the feasible region.
I completed the quiz
Answer:
at the vertices of the feasible region
Step-by-step explanation:
this is the correct answer
hope i helped
What degree of rotation about the origin will cause the triangle below to map
onto itself?
A. 90 degrees
B. 360 degrees
C. 180 degrees
D. 270 degrees
Answer: 360ᴼ
Step-by-step explanation:
If a figure goes 360ᴼ around the graph, it will be mapped onto itself.
360ᴼ is full circle (number of degrees in a circle), so the figure just went around in a circle, back into the same location before it rotated.
Answer:
360
Step-by-step explanation:
i took the text
Two positive, consecutive, odd integers have a product of 143.
Complete the equation to represent finding x, the greater integer.
x(x –
) = 143
What is the greater integer?
Answer:
The answer is 13
Step-by-step explanation:
Two positive and consecutive old numbers are x and x - 2.
=> x(x - 2) = 143
=> x^2 - 2x - 143 = 0
=> x^2 + 11x - 13x - 143 = 0
=> x(x + 11) - 13(x + 11) = 0
=> (x + 11)(x - 13) = 0
=> x = -11 (invalid)
or x = 13 (valid), the remaining number is 13 - 2 = 11
=> The two numbers are 11 and 13, and the greater number is 13.
Hope this helps!
:)
Answer:
top: 2
bottom: 13
Step-by-step explanation:
step
by
step
explanation
"Two purple sea slugs are mated with each other. Among their numerous offspring, 428 have a purple integument and 152 have orange integuments. With a chi-square test, compare the observed numbers with a 3:1 ratio and determine if the difference between observed and expected could be a result of chance."
Answer:55
Step-by-step explanation:
55x1=55
The base of a rectangular prism has an area of 24 square millimeters. The volume of the prism is 144 cubic millimeters. The shape is a cube. What is the height of the prism?
Answer:
height = 6 mm
Step-by-step explanation:
The prism is a rectangular prism. The base area of the prism is 24 mm². The volume of the prism is given as 144 mm³.
The height of the prism can be solved as follows.
Volume of the rectangular prism = Bh
where
B = base area
h = height
Volume = 144 mm³
B = 24 mm²
volume = Bh
144 = 24 × h
144 = 24h
divide both sides by 24
h = 144/24
h = 6 mm
Answer:
c
Step-by-step explanation:
edg 2022
if two adjecent complentary angles are congruent then what is the measure of each angle?
Consider the following quadratic equation: 25x2=36 Using the standard form ax2+bx+c=0 of the given quadratic equation, factor the left hand side of the equation into two linear factors.
Answer:
(5x -6)(5x +6) = 0
Step-by-step explanation:
Subtract 36 to put the equation in standard form. In this form, it looks like the difference of squares, so can be factored as such.
25x^2 -36 = 0
(5x)^2 -6^2 = 0
(5x -6)(5x +6) = 0
The histogram represents the daily low and high temperatures in a city during March. Which comparison of the distributions is true?
A)The distribution of low temperatures is nearly symmetric, and the distribution of high temperatures is nearly symmetric.
B)The distribution of low temperatures is skewed right, and the distribution of high temperatures is nearly symmetric.
C)The distribution of low temperatures is nearly symmetric, and the distribution of high temperatures is skewed right.
D)The distribution of low temperatures is skewed right, and the distribution of high temperatures is skewed right.
Answer:
ITS C
Step-by-step explanation:
The other answer is wrong, I just tried it.
Answer:
It's C on EDG
Step-by-step explanation:
Given the coordinates (0,0) and (4, 1), the distance is:
Answer:
[tex]\sqrt{17}[/tex] or ≈4.12
Step-by-step explanation:
Use the distance formula
d= √(x₂ - x₁) ² + (y₂-y₁) ²
d= √(4-0)² + (1-0)²
d= √16 + 1
d= √17
Which product represents the fraction of the circle that is shaded?
A
B
C
D
Answer:
B
Step-by-step explanation:
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
D. Time ( length)
Step-by-step explanation:
The function is measuring the length of the race, and the time it took to complete. So, it would be D.
// have a great day //
Answer:
D. Time(length)
Step-by-step explanation:
→The time is on the outside because, according to the information that has been given/provided, the length of the race depends on the time taken to complete the race.
This means the correct answer is "D. Time(length)."
J.D. Power and Associates conducts vehicle quality surveys to provide automobile manufacturers with consumer satisfaction information about their products (Vehicle Quality Survey, January 2010 ). Using a sample of vehicle owners from recent vehicle purchase records, the survey asks the owners a variety of questions about their new vehicles, such as those shown below. For each question, state whether the data collected are categorical or quantitative and indicate the measurement scale being used.
a. What price did you pay for the vehicle?
b. How did you pay for the vehicle? (Cash, Lease, or Finance)
c. How likely would you be to recommend this vehicle to a friend? (Definitely Not, Probably Not, Probably Will, and Definitely Will)
d. What is the current mileage?
e. What is your overall rating of your new vehicle? A 110 -point scale, ranging from I for
unacceptable to 10 for truly exceptional, was used.
Answer:
Categorical data includes
b. How did you pay for the vehicle? (Cash, Lease, or Finance)
c. How likely would you be to recommend this vehicle to a friend? (Definitely Not, Probably Not, Probably Will, and Definitely Will)
e. What is your overall rating of your new vehicle? A 1 to 10 point scale, ranging from I for unacceptable to 10 for truly exceptional, was used.
Quantitative data includes
a. What price did you pay for the vehicle?
d. What is the current mileage?
Step-by-step explanation:
Categorical data refers to the kind of data in which the variables are grouped based on a particular quality, ticking a particular box or satisfying some specific requirements.
It uses one or more qualitative property/properties to assign variables into a limited, usually fixed groups or categories. Note that the qualitative property might be a grouped data of numerical values. As long as there are easily separable and recognizable groups, it is categorical data.
This is also called qualitative data.
Quantitative data is a data that is strictly about numerical values. A dataset that consists of numerical values of the members of the dataset. Deals almost exclusively with numbers, usually ungrouped.
So, examining the given datasets one at a time
a. What price did you pay for the vehicle?
The answer to this question is a numerical value and for various customers, it builds up a dataset of strictly numerical values. Hence, this resulting data is a quantitative data.
b. How did you pay for the vehicle? (Cash, Lease, or Finance)
The answers to this question can only take 3 forms; Cash, Lease or Finance, indicating that all the variables in the dataset can only take on limited, fixed number of groups/categories. Hence, this dataset is a categorical data.
c. How likely would you be to recommend this vehicle to a friend? (Definitely Not, Probably Not, Probably Will, and Definitely Will)
The answers to this question too can take on 4 limited, fixed categories or groups, Hence, it's easy to see that this dataset is also categorical data.
d. What is the current mileage?
The answer to this question is a numerical value. Various answers from numerous persons would lead to a data of numbers. Hence, this is a quantitative data.
e. What is your overall rating of your new vehicle? A 1 to 10 point scale, ranging from I for unacceptable to 10 for truly exceptional, was used.
Limited, fixed categories or groups (10 groups) are also available for this data, hence, it is easily a categorical data.
Hope this Helps!!!